New physical interpretation of the Bel-Robinson tensor

A short presentation of the gauge theory of gravitation with quadratic Lagrangian Lsub(g)=(c4/16πG)(Ωsub(.j)sup(j)Λetasub(i)sup(j)+THETAsup(i)Λ*THETAsub(i))+((h/2π)/16π)Ωsub(.j)sup(i)Λ*Ωsub(.i)sup(j), where (h/2π) is the Planck constant; c is the velocity of light in vacuum, G means the Newtonian gravitational constant and Ωsub(.j)sup(i) and THETAsup(i) are the curvature and torsion 2-forms respectively, is given. Then, the new physical interpretation of the so-called Bel-Robinson tensor in the framework of the theory is presented; namely, the Bel-Robinson tensor multiplied by the constant β=(h/2π)c/16π is physically interpreted as the 4-index energy-momentum tensor of the vacuum and torsionless gauge field Rsub(.klm)sup(i). (author)